Stability of linear systems with delayed state An LMI approach

This paper focuses on the problem of asymptotic stability of a class of time-delay systems described by linear delayed state equations involving several constant (or time-varying), but unknown delays. A sufficient delays-dependent stability condition of the considered system is given using a Lyapunov-Razumikhin function approach, Futhermore, by transforming the stability problem into a linear matrix inequality optimisation problem, the approach adopted here allows the computation of a suboptimal largest ellipsoidal stability region in the delays parameter space such that the asymptotic stability of the time-delay system is ensured